用Laplace变换求Kratzer势径向波函数的二类递推关系

Recursive Relations of the Kratzer Potential's Radial Wave Function via Laplace Transform

求解了Kratzer势的Schrdinger方程,得到了归一化的波函数和能量方程.用Laplace变换使径向的二阶微分方程退化为一阶微分方程,直接积分后用级数展开,应用Laplace逆变换得出本征函数.另外,用Laplace变换方法给出了径向波函数关于量子数N和角量子数L的二类递推关系.

In this paper the exact bound state solutions including the energy equation and normalized wave function of Schr＇odinger equation with the Kratzer potential is obtained. By using the Laplace transformation this second - order differential equation can be reduced to the first - order case and then the eigenfunction can be derived from direct integral and a simple series expansion via Laplace inverse transform. In addition, two kinds of recursive relations about the principle and angular quantum numbers N and L for the radial wave function are also given by using the same method.